|
This article is cited in 6 scientific papers (total in 6 papers)
Convergence of formal Dulac series satisfying an algebraic ordinary differential equation
R. R. Gontsovab, I. V. Goryuchkinac a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
b National Research University "Moscow Power Engineering Institute", Moscow, Russia
c Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
Abstract:
A sufficient condition is proposed which ensures that a Dulac series that formally satisfies an algebraic ordinary differential equation (ODE) is convergent. Such formal solutions of algebraic ODEs are quite common: in particular, the Painlevé III, V and VI equations have formal solutions given by Dulac series; they are convergent in view of the sufficient condition presented.
Bibliography: 13 titles.
Keywords:
algebraic ODE, formal solution, Dulac series, convergence.
Received: 09.01.2018 and 28.01.2019
Citation:
R. R. Gontsov, I. V. Goryuchkina, “Convergence of formal Dulac series satisfying an algebraic ordinary differential equation”, Sb. Math., 210:9 (2019), 1207–1221
Linking options:
https://www.mathnet.ru/eng/sm9064https://doi.org/10.1070/SM9064 https://www.mathnet.ru/eng/sm/v210/i9/p3
|
|